# Approximate Isomorphism of Metric Structures

@article{Hanson2020ApproximateIO, title={Approximate Isomorphism of Metric Structures}, author={James Hanson}, journal={arXiv: Logic}, year={2020} }

We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov and by Ben Yaacov, Berenstein, Henson, and Usvyatsov, which are largely incompatible. With this we explicitly exhibit Scott sentences for the perturbation systems of the former paper, such as the Banach-Mazur distance and the Lipschitz distance between metric spaces. Our formalism is simultaneously characterized syntactically by a mild generalization of perturbation…

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